In this project we study the stabilization of some suspension-bridge problems in order to obtain some certitudes from the response and suggestions for future designs. Our aim is to investigate the effects of a localized strong damping (Voight damping), a viscoelastic damping and the effect of heat on the stability of the model and establish general decay rate results. Our tool for that is the use of multiplier method. The results of this work, if obtained, will give an idea to engineers to stabilize bridges with an optimal coast; and open the door for further research in this direction.